A Neural-Network surrogate for microstructure dynamics and crystal growth

Given their potential as universal approximators, Neural Networks (NN) are nowadays used across all fields of scientific research to formulate predictions on complex systems. While their exploitation for atomistic simulations is quite a common practice, it is only in the last few years that NN approaches have found application for accelerating or fully surrogating numerical simulations of materials evolution at the mesoscale [1]. Here we show how a Convolutional Recurrent NN [2] can successfully provide quantitative approximation of the evolution sequences being solution of partial differential equations. A data-driven approach is pursued, using suitably large datasets of “true” evolution images, computed by conventional numerical methods, to train the NN model. Physics-based regularizations are also considered to enhance convergence. The approach is demonstrated for a few fundamental case studies of morphological and microstructural evolution of crystalline materials including phase-separation dynamics [3] and crystal growth, either in 2D and 3D. The major advantage of using NN surrogate models stems from their ability of matching the accuracy of the explicit numerical solution methods used for their training at a fraction of the computational costs. This returns significant speed-ups of the simulations, even reaching a factor of three orders of magnitude for our 3D models. Moreover, the possibility of generalization on larger domain sizes and for timescales well beyond the training ones is also key to approach more realistic applications. The performances of the trained models are then evaluated with respect to the extent of such achievements and the advantages and weaknesses of the proposed strategy are critically discussed. [1] Yang K., Cao, Y., Zhang Y., Fan. S, Tang. S, Aberg D., Sadigh B., Zhou F. Patterns 2 (2021) 100243 [2] Lanzoni D., Albani M., Bergamaschini R., Montalenti F. Phys. Rev. Mater. 6 (2022) 103801 [3] Lanzoni D., Fantasia A., Bergamaschini R., Pierre-Luis O., Montalenti F., Mach. Learn.: Sci. Technol. 5 (2024) 045017